Sums of Reciprocals
A set of integers is said to be small if the sum of its reciprocals converges to a finite value. For instance, by the prime number theorem, the prime numbers are not small. Paul Erdős (1962) proved that every sum-free sequence is small, and asked how large the sum of reciprocals could be. For instance, the sum of the reciprocals of the powers of two (a geometric series) is two.
If denotes the maximum sum of reciprocals of a sum-free sequence, then through subsequent research it is known that .
Read more about this topic: Sum-free Sequence
Famous quotes containing the word sums:
“At Timon’s villalet us pass a day,
Where all cry out,What sums are thrown away!’”
—Alexander Pope (1688–1744)